Abstract
Cross-recurrence quantification analysis (CRQA) is a powerful nonlinear time-series method to study coordination and cooperation between people. This chapter concentrates on two methodological issues related to CRQA on categorical data streams, which are commonly encountered in the behavioral sciences . Firstly, we introduce a more general definition of recurrence as ‘behavioral matching ’, which can be applied to several kinds of matches simultaneously, visualized by a color coding. We will refer to this as cross -matching, and to the resulting quantification procedure as Chromatic CRQA . Secondly, cross-recurrence plots of categorical data often prominently consists of rectangular structures. This calls for a differential analysis of vertical and horizontal lines, rather than of diagonal lines. We introduce a simple procedure for this, referred to as Anisotropic CRQA . Both procedures are demonstrated with empirical studies on children’s problem-solving behavior and by means of a model simulation. The authors hope that the ideas presented here increase the power and applicability of CRQA in the behavioral sciences, and that this chapter serves as a stepping stone for their mathematical and methodological development.
Keywords
- Line Structure
- Dyadic Interaction
- Behavioral Category
- Recurrence Quantification Analysis
- Phase Space Reconstruction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes
- 1.
Note that recoding the data oftentimes will also do the trick. However, complex cases with multiple matches and non-matches require a more general and powerful approach. Interestingly, this also gives rise to a set of additional measures, as will become clear further on.
- 2.
These tests can readily be applied to small sample sizes or unequal groups of data, in this case to determine the statistical significance (p-value) of the differences between the line structures. The test repeatedly (e.g., 1000 times) compares the observed difference to the difference found within a range of simulated data drawn from the original sample. The p-value is computed by dividing the number of times the observed or a bigger difference occurs in these random samples by the number of drawn samples.
- 3.
- 4.
In fact written in this way the system models a system of three asymmetrically coupled Kuramoto oscillators under a specific set of parameter settings, among which, in particular equal intrinsic frequency.
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Acknowledgment
The first author wishes to express his appreciation to Fred Hasselman, for the many fruitful discussions arising from shared encounters with the methodological issues regarding recurrence analysis on categorical behavioral time series.
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Cox, R.F.A., van der Steen, S., Guevara, M., de Jonge-Hoekstra, L., van Dijk, M. (2016). Chromatic and Anisotropic Cross-Recurrence Quantification Analysis of Interpersonal Behavior. In: Webber, Jr., C., Ioana, C., Marwan, N. (eds) Recurrence Plots and Their Quantifications: Expanding Horizons. Springer Proceedings in Physics, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-319-29922-8_11
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